Hi:
I was wondering if someone can explain the concept behind positive and negative power supply voltages ? For example some devices can accept +5V and -5V. Is this strictly for polarity purposes ? The magnitude is 5V in either case, I understand.

And, why do some devices accept 2 different types of inputs while others only accept one ? For example, one device accepts 5V while another accepts +- 5V ?

One example of the usage of negative voltage is to increase switching speeds in digital circuits.
Most multiplexers have the +5V Vcc and ground (0 V) power pins but some multiplexers also have a negative -5 voltage pin for the sole purpose of enabling certain transistors within the circuit to switch faster on/off. You can look up emitter coupled logic for more details.

Voltage is defined as the energy each charge aquires when moving from a to b. I assume you havent taken physics courses in electromagnetism so i'll try not to complicate things.

The term voltage is a bit difficult to grasp at first because it's all about relative voltages. Let's describe voltage between 2 points as the tendency of charge to move between those 2 points. If we arbitrary choose location B to be at zero volts and location A at 10 volts. The charge will have a motive to move from A to B (from higher to lower voltage).
We chose 0 and 10V for simplicity but we could aswell have chosen B to be at 30V and A at 40V. The voltage difference however is still 10V as before and the charge will have the same tendancy as before (0 and 10V) to move from A to B.

So let's imagine a circuit with 3 points A, B and C which have voltages +5V, 0V and -5V in the same order.

The voltage difference between A and B is 5V. As mentioned before you can look at this as the tendency for the charges to move between the locations. You might have realised by now that the voltage difference between A and C is 10 volts. (5V-(-5V)) = 10V. So the charges have an even greater motive to move from A to C then from A to B (actually double the tendency).

Zero voltage is always decided at an arbitrary location (we can choose any location we want as long as relative voltages are maintained). Conventionally this is what we call ground. Usually when you look at a circuit you imagine the current flowing from a source with positive voltage to ground (0V).

In order to have positive and negative voltages, you must first define what your reference point is. In many cases, earth ground is a very good 0V level, but that need not always be the case.

In a battery operated system, you can define the positive side, negative side or middle of the battery voltage to be your 0V level. Depending on what you choose your 0V level to be, the other voltages become mathematically positive or negative with respect to it.

In a battery operated system with 2 9V batteries, you can define the system multiple ways.

0V -battery+ 9V -battery+ 18V

-9V -battery+ 0V -battery+ 9V

-18V -battery+ -9V -battery+ 0V

Now you can also connect you 0V to earth ground and change the batteries to other power sources or storage elements.

Certainly. You can make a virtual ground at the midpoint of the supply. Just remember that the virtual ground and the ground on your supply, and possibly other test equipment, are not the same. The inputs and outputs will have to be adjusted accordingly.

Or, you can use a DC/DC converter to give you an isolated +/-9V supply and then ground the center voltage.

That is right. Use a resistor divider to create the new "ground" voltage and follow it with another op amp, which can be as simple as connecting divider voltage to (+) terminal and connecting output of the op amp to the (-) terminal, so that it becomes a point that can source and sink current without altering the divider voltage.